Electroencephalography and Identification of Transfer Functions in a Feedback System

Identification of Transfer Function in a Feedback System and Autoregressive Analysis

Identification of transfer function matrices in a feedback system is discussed by using the singular value decomposition of Hankel matrix from the viewpoint of inverse problems. A method of model reduction is considered, and selection criteria are proposed for identification of them. Transformation formula between open loop and closed loop transfer function matrices are determined from the feedback loop structure, and they are needed for identification of open loop transfer function matrices under such a condition where the feedback system is in a minimum phase. Though the identifiability of open loop transfer function matrices can be examined in the framework of innovation model equivalent to the feedback system, there are pole-zero cancellations in the identification of them. The method to reduce a model order of an open loop transfer function is discussed by using the singular value decomposition of a gramian given by the open loop transfer function with higher degree. To check reliability of the present algorithm, a simulation study is performed for an example.

A unified theory of identification in a feedback system is presented from the viewpoint of inverse problem on reactor noise. A power reactor described by a 4 block feedback model is expressed in terms of equivalent correlation functions as a 5 block feedback model with an additional loop, if one of subsystems of the reactor becomes unstable, however, the total system is stable by negative feedback effects, and if noise sources are not independent. The addition of a loop in the feedback system leads errors in estimation of open loop transfer functions. In the case, modified open loop transfer functions are identified instead of original ones. From the viewpoint of reactor diagnosis, notes on system identification are discussed on an open loop transfer function in a low power reactor and on effects of diagonalization in covariance space of noise sources.

Identification of transfer functions and statistical inverse problems

The paper presents a systematic approach for finding the optimal set of predictors for consistent identification of a single transfer function in an acyclic dynamic network. It is assumed that the topology of the network is known, the forcing inputs are not measured, and the observations have positive additive costs. For a class of networks where the target node is not involved in a feedback loop, sufficient and necessary conditions are derived to consistently identify a certain transfer function via a multi-input single-output prediction error method. This enables designing a systematic graphical approach based on the notion of d-separation to look for an optimal set of predictors that minimizes an appropriate additive cost function. It is shown that the required conditions for consistency and optimality are equivalent to the notion of separation in an undirected graph resulted from systematically manipulating the graphical representation of the network. Then, some well-known algorithms from computer science can be used to find the optimal set of predictors.

l1 Robust Identification of Fractional Transfer Functions

From the viewpoint of stochastic inverse problem, identification of transfer functions in feedback systems has been examined by the previous papers[1][2], and applied to EEG analysis[3]. Some transfer functions between measurement regions are identified by our method of inverse problem in a stochastic feedback system. However, there are still open problems of our method for stochastic inverse problem: One problem is that there occurs a chaos-like behavior in matrix Riccati equation and it affects a property of identified innovation model. The other is a filtering effect on transfer functions for pre-processing of high pass filter. These problems are discussed from the viewpoint of statistical inverse problem.

A new tuning method for Fractional Order Controllers (FOC) based on Bode’s ideal transfer function as a reference model is proposed in this paper. The proposed fractional order controller parameters are obtained by a simple tuning technique in two steps. In the first step, the open loop reference fractional integrator is designed according to the desired performances, and then approximated by a rational transfer function using Charef’s or Oustaloup’s approximation method. In the second step, a standard pole placement technique is used to align each pole of the plant transfer function with the nearest one of the Rational Function Approximation (RFA). The FOC transfer function is then obtained by gathering the remained poles and zeros of the RFA. The most innovative character of the proposed method is its simplicity and its remarkable performances in terms of robustness towards the variation of the static gain. Simulation of some illustrative examples confirms and validates the proposed method.

A practical method of assessing ultrasonic A-scan pulse-echo scanner performance is described, which relies upon the identification and quantitation of an overall system transfer function. The mapping of reflecting elements into an image is then described by this transfer function, and indices of system performance, and particularly resolution and range accuracy, are developed in terms of the shape of the transfer function. Some advantages of this method compared to more conventional methods of assessing scanner performance are discussed.

An optimal algorithm for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented. The proposed method is based on the minimization of the l/sub 2/-norm of the true fitting error and is uniformly applicable for rational models with arbitrary numbers of poles and zeros. Existing methods either modify the true nonlinear error criterion in the theoretical derivation or require the transfer function model to have exactly one less number of zeros than poles. The multidimensional nonlinear error criterion is decoupled into a purely linear and a nonlinear subproblem of reduced dimension. The inherent mathematical structure in the non-linear subproblem is exploited in formulating an efficient iterative computational algorithm for its minimization. The effectiveness of the algorithm is demonstrated with several simulation examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Automated On-Line Frequency Domain Identification and Genetic Estimation of Plant Transfer Functions

The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration and reduce pipeline damage. First, a mathematical model of the distributed piping system was established using the finite element analysis method, and the characteristics of the distributed piping system were studied effectively. Further, the time-frequency domain parameter identification method was used to realise the system identification of the cross-point vibration transfer function between the brake and sensor, and the particle swarm optimisation algorithm was utilised to further optimise the transfer function parameters to improve the system identification accuracy. Therefore, a fractional-order PID controller was designed using the D-decomposition method, and the optimal controller parameters were obtained. The experimental and numerical simulation results show that the improved system identification algorithm can significantly improve modelling accuracy. In addition, the designed fractional-order PID controller can effectively reduce the system’s overshoot, oscillation time, and adjustment time, thereby reducing the vibration response of piping systems.

L2-overbiased, L2-underbiased and L2-unbiased estimation of transfer functions

A practical method for the consistent identification of a module in a dynamical network

For the purpose of research, modelling and simulation of control plants, linear models are commonly used. There are many methods of creating linear models of plant dynamics. Artificial intelligence methods are used in many areas of science and technology. There are also several known applications of artificial intelligence in automatic controllers. The authors have developed a method of linear modelling by means of evolutionary algorithms, which enable searching for optimal values of the transfer function coefficients. For a method validation, an experiment with a real thermal plant was conducted. This paper presents identification of a linear transfer function of a thermal plant.